/* --------------------------------------------------------------------------
CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-17 Bradley M. Bell

CppAD is distributed under multiple licenses. This distribution is under
the terms of the
                    Eclipse Public License Version 1.0.

A copy of this license is included in the COPYING file of this distribution.
Please visit http://www.coin-or.org/CppAD/ for information on other licenses.
-------------------------------------------------------------------------- */

/*
$begin checkpoint.cpp$$
$spell
	checkpointing
	Taylor
$$

$section Simple Checkpointing: Example and Test$$

$head Purpose$$
Break a large computation into pieces and only store values at the
interface of the pieces.
In actual applications, there may be many functions, but
for this example there are only two.
The functions
$latex F : \B{R}^2 \rightarrow \B{R}^2$$
and
$latex G : \B{R}^2 \rightarrow \B{R}^2$$
defined by
$latex \[
	F(y) = \left( \begin{array}{c}
		y_0 + y_0 + y_0
		\\
		y_1 + y_1 + y_1
	\end{array} \right)
	\; , \;
	G(x) = \left( \begin{array}{c}
		x_0 \cdot x_0 \cdot x_0
		\\
		x_1 \cdot x_1 \cdot x_1
	\end{array} \right)
\] $$

$code
$srcfile%example/atomic/checkpoint.cpp%0%// BEGIN C++%// END C++%1%$$
$$


$end
*/
// BEGIN C++

# include <cppad/cppad.hpp>

namespace {
	using CppAD::AD;
	typedef CPPAD_TESTVECTOR(AD<double>)            ADVector;
	typedef CppAD::atomic_base<double>::option_enum option_enum;

	void f_algo(const ADVector& y, ADVector& z)
	{	z[0] = 0.0;
		z[1] = 0.0;
		for(size_t k = 0; k < 3; k++)
		{	z[0] += y[0];
			z[1] += y[1];
		}
		return;
	}
	void g_algo(const ADVector& x, ADVector& y)
	{	y[0] = 1.0;
		y[1] = 1.0;
		for(size_t k = 0; k < 3; k++)
		{	y[0] *= x[0];
			y[1] *= x[1];
		}
		return;
	}
	bool test_case(
		option_enum f_sparsity, option_enum g_sparsity, bool optimize )
	{	bool ok = true;
		using CppAD::checkpoint;
		using CppAD::ADFun;
		using CppAD::NearEqual;
		size_t i, j, k, n = 2, m = n;
		double eps = 10. * std::numeric_limits<double>::epsilon();

		// checkpoint version of the function F(x)
		ADVector ax(n), ay(n), az(m);
		for(j = 0; j < n; j++)
			ax[j] = double(j + 1);
		// could also use bool_sparsity_enum or set_sparsity_enum
		checkpoint<double> atom_f("atom_f", f_algo, ax, ay, f_sparsity);
		checkpoint<double> atom_g("atom_g", g_algo, ay, az, g_sparsity);

		// Record a version of z = g[f(x)] without checkpointing
		Independent(ax);
		f_algo(ax, ay);
		g_algo(ay, az);
		ADFun<double> check_not(ax, az);

		// Record a version of z = g[f(x)] with checkpointing
		Independent(ax);
		atom_f(ax, ay);
		atom_g(ay, az);
		ADFun<double> check_yes(ax, az);

		// checkpointing should use fewer operations
		ok &= check_yes.size_var() < check_not.size_var();

		// this does not really save space because f and g are only used once
		ok &= check_not.size_var() <=
			check_yes.size_var() + atom_f.size_var() + atom_g.size_var();

		// compare forward mode results for orders 0, 1, 2
		size_t q = 2;
		CPPAD_TESTVECTOR(double) x_q(n*(q+1)), z_not(m*(q+1)), z_yes(m*(q+1));
		for(j = 0; j < n; j++)
		{	for(k = 0; k <= q; k++)
				x_q[ j * (q+1) + k ] = 1.0 / double(q + 1 - k);
		}
		z_not = check_not.Forward(q, x_q);
		z_yes = check_yes.Forward(q, x_q);
		for(i = 0; i < m; i++)
		{	for(k = 0; k <= q; k++)
			{	double zik_not = z_not[ i * (q+1) + k];
				double zik_yes = z_yes[ i * (q+1) + k];
				ok &= NearEqual(zik_not, zik_yes, eps, eps);
			}
		}

		// compare reverse mode results
		CPPAD_TESTVECTOR(double) w(m*(q+1)), dw_not(n*(q+1)), dw_yes(n*(q+1));
		for(i = 0; i < m * (q + 1); i++)
			w[i] = 1.0 / double(i + 1);
		dw_not = check_not.Reverse(q+1, w);
		dw_yes = check_yes.Reverse(q+1, w);
		for(j = 0; j < n; j++)
		{	for(k = 0; k <= q; k++)
			{	double dwjk_not = dw_not[ j * (q+1) + k];
				double dwjk_yes = dw_yes[ j * (q+1) + k];
				ok &= NearEqual(dwjk_not, dwjk_yes, eps, eps);
			}
		}

		// compare forward mode Jacobian sparsity patterns
		CppAD::vector< std::set<size_t> > r(n), s_not(m), s_yes(m);
		for(j = 0; j < n; j++)
			r[j].insert(j);
		s_not = check_not.ForSparseJac(n, r);
		s_yes = check_yes.ForSparseJac(n, r);
		for(i = 0; i < m; i++)
			ok &= s_not[i] == s_yes[i];

		// compare reverse mode Jacobian sparsity patterns
		CppAD::vector< std::set<size_t> > s(m), r_not(m), r_yes(m);
		for(i = 0; i < m; i++)
			s[i].insert(i);
		r_not = check_not.RevSparseJac(m, s);
		r_yes = check_yes.RevSparseJac(m, s);
		for(i = 0; i < m; i++)
			ok &= r_not[i] == r_yes[i];


		// compare reverse mode Hessian sparsity patterns
		CppAD::vector< std::set<size_t> > s_one(1), h_not(n), h_yes(n);
		for(i = 0; i < m; i++)
			s_one[0].insert(i);
		h_not = check_not.RevSparseHes(n, s_one);
		h_yes = check_yes.RevSparseHes(n, s_one);
		for(i = 0; i < n; i++)
			ok &= h_not[i] == h_yes[i];

		return ok;
	}
}

bool checkpoint(void)
{	bool ok = true;

	// different types of sparsity
	option_enum pack_sparsity = CppAD::atomic_base<double>::pack_sparsity_enum;
	option_enum bool_sparsity = CppAD::atomic_base<double>::bool_sparsity_enum;
	option_enum set_sparsity  = CppAD::atomic_base<double>::set_sparsity_enum;

	// test some different cases
	ok &= test_case(pack_sparsity, pack_sparsity, true);
	ok &= test_case(pack_sparsity, bool_sparsity, false);
	ok &= test_case(bool_sparsity, set_sparsity,  true);
	ok &= test_case(set_sparsity,  set_sparsity,  false);

	return ok;
}
// END C++
